Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Rational Equations
3:43 minutes
Problem 79b
Textbook Question
Textbook QuestionSolve the variation problems in Exercises 77–82. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Variation
Inverse variation describes a relationship where one variable increases as the other decreases. In mathematical terms, if two variables x and y vary inversely, their product is constant (xy = k). This concept is crucial for solving problems where one quantity affects another in an opposite manner, such as the relationship between pitch and wavelength in this question.
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Wavelength and Frequency
Wavelength and frequency are fundamental concepts in wave physics, particularly in sound and light. Wavelength is the distance between successive crests of a wave, while frequency refers to the number of vibrations or cycles per second, measured in hertz (Hz). Understanding how these two quantities relate is essential for solving problems involving sound waves, as they are inversely related in the context of pitch.
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Proportional Relationships
Proportional relationships occur when two quantities maintain a constant ratio. In the context of the problem, the pitch of a tone and its wavelength are inversely proportional, meaning that as one increases, the other decreases. Recognizing this relationship allows for the application of proportional reasoning to find unknown values, such as determining the pitch for a different wavelength.
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